In higher dimensional quantum field theory, irreducible representations of the Poincare group are associated with particles. Their counterpart in two-dimensional massless models are "waves" introduced by Buchholz. In this paper we show that waves do not interact in two-dimensional Moebius covariant theories and in- and out-asymptotic fields coincide. We identify the set of the collision states of waves with the subspace generated by the chiral components of the Moebius covariant net from the vacuum. It is also shown that Bisognano-Wichmann property, dilation covariance and asymptotic completeness (with respect to waves) imply Moebius symmetry.
Under natural assumptions, we observe that the maps which give asymptotic fields in Poincare covariant theory are conditional expectations between appropriate algebras. We show that a two-dimensional massless theory is asymptotically complete and noninteracting if and only if it is a chiral Moebius covariant theory.
Monochromatic plane-fronted waves in conformal gravity are pure gauge
在广义相对论的共形不变理论中，我们考虑了闵可夫斯基背景下的面前单色引力波。这里我们指的是以下形式的波：$g_{μν}=η_{μν}+ε_{μν}F(k\cdotx)$，其中$ε_{μν}$是一个恒定的偏振张量，$k_μ$是一个类光矢量。我们还假定坐标规范条件$|g|-1/4\partial_τ(|g|1/4g^{στ})=0$是调和规范条件$g^{μν}Γ_{μν}^σ=-|g|-1/2\partial_τ(|g|1/2g^{στ})=0, where $ \det [ g_{μν} ] \equivg $. Requiring additionally the conformal gauge condition $ g=-1 $ surprisingly implies that the waves are both transverse and traceless. Although the ansatz for the metric is eminently reasonable when considering perturbative gravitational waves, we show that the metric is reducible to the metric of Minkowski space-time via a sequence of coordi…
